Continuity mistake: At the beginning of the show, the hospital Mr. Burns is at has a sign in front of it that reads, "Got Tumor?", but when we see the hospital again it isn't there. Additionally, the "Mayo Clinic" sign atop the building gets noticeably smaller in the second shot.
Continuity mistake: When Moe is going to get a plastic surgery, the surgeon draws some marks on his face. You see Moe from a side view, and the marks on his face aren't visible from that angle. However, the marks on his face suddenly appear and you can now see them from that angle.OL1V3R666
Continuity mistake: In "I Know What You Diddly-Iddly Did", there are a few errors: Homer says, "Guess I forgot to put the fog lights in" at a slightly higher pitch to when we heard him say it earlier (When the event actually happened). When Marge actually ran over Ned she did not carry on driving. The flashback shows that Ned was run over without glasses. However in the actual event he had glasses on.OL1V3R666
Continuity mistake: When the Ranger stops the Simpsons' car at the start of the episode, watch his "class ring". When he puts his hands inside the car it's on the left hand. However, the flies later eat his hand and take his ring, and it's suddenly his right hand they ate and took it from.David Mercier